Thread: CORRELATE help - information outside of correlation window

Started: 2019-06-18 15:43:33
Last activity: 2019-06-19 09:51:55
Topics: SAC Help
Mitchell Liddell
2019-06-18 15:43:33
Hello,

I have a problem with the CORRELATE function in sac.

I imagine the correlation function performing a marching dot product
between the two time series, and filling in zeros at the end/beginning as
necessary when the shift of the one time series exceeds the boundary of the
other. This is a "Cut, shift, correlate" order of operations and must
artificially lower the correlation coefficient at greater time shifts.

Is there any way for information outside of the original window to be
included in the correlation? That is, If I want the correlation from T1 to
T2, is there some way for the time series to be shifted *before* being cut,
or dynamically, so real data are always being compared at every time shift
and there is no infill of zeros?

I hope I have explained what I am asking clear enough, please let me know
if this makes sense and if you have any suggestions!

--
Mitch V. Liddell, PhD
Postdoctoral Researcher
University of Alberta
587-372-5060

  • Dear All -

    Two suggestions that come to mind are: 1) to throw away some of your data in order to ensure the correlations are never zero-padded, and 2) to extrapolate samples using an autoregressive model (AR or ARMA) estimated from the autocorrelation up to the end of your data.

    You can do the first one in SAC by using the CUTIM command on a trace to make a set of cuts at different lags from the start time (multiple cuts in the same trace are possible) and then by using CORRELATE (with one window covering the whole data span) to get a series of correlations corresponding to different lags.

    The second approach requires significantly more work (I’d recommend reading Jenkins and Watts for what you need to know) but if every bit of your data is sacred, it could be worth the effort. Extrapolating for long stretches is, um, questionable.

    On 18 Jun 2019, at 22:47, Mitchell Liddell <liddell<at>ualberta.ca> wrote:

    Hello,

    I have a problem with the CORRELATE function in sac.

    I imagine the correlation function performing a marching dot product between the two time series, and filling in zeros at the end/beginning as necessary when the shift of the one time series exceeds the boundary of the other. This is a "Cut, shift, correlate" order of operations and must artificially lower the correlation coefficient at greater time shifts.

    Is there any way for information outside of the original window to be included in the correlation? That is, If I want the correlation from T1 to T2, is there some way for the time series to be shifted *before* being cut, or dynamically, so real data are always being compared at every time shift and there is no infill of zeros?

    I hope I have explained what I am asking clear enough, please let me know if this makes sense and if you have any suggestions!

    --
    Mitch V. Liddell, PhD
    Postdoctoral Researcher
    University of Alberta
    587-372-5060

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